Explanation Given: The given family of curves is 2 x − 3 y = C . Concept used: At point P afamily of curves f ( x , y ) = C will meet to family of orthogonal trajectories. At P x = X , y = Y , the slope d Y d X of the orthogonal trajectories is obtained by d Y d X = [ − 1 d y d x ] ( X , Y ) where d y d x is the slope of the given family of curves f ( x , y ) = C . The orthogonal trajectories will be obtained by integrating d Y d X = − 1 f ′ ( x , y ) . Calculation: Consider the given family of curves. 2 x − 3 y = C Differentiate the above equation

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 5.6, Problem 33PS

To determine

Tofind:the orthogonal trajectories of the given family of curves. Also sketch several members of the family of orthogonal trajectories and the family of given curves on same coordinate axes.

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Chapter 5.6, Problem 32PS

Chapter 5.6, Problem 34PS

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1. Find an equation of a curve, such that at each point (x, y) on the curve, the slope equals twice the square of the distance between the point and the y-axis and the point (-1,2) is on the curve. *

Chapter 5 Solutions

Calculus

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Tofind: the orthogonal trajectories of the given family of curves. Also sketch several members of the family of orthogonal trajectories and the family of given curves on same coordinate axes.

Solution Summary: The author analyzes the orthogonal trajectories of the given family of curves.

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Tofind:the orthogonal trajectories of the given family of curves. Also sketch several members of the family of orthogonal trajectories and the family of given curves on same coordinate axes.

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Chapter 5 Solutions